Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems

Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information useful for understanding dynamics. However, Koopman operators can have continuous spectra and infinite-dimensional invariant subspaces, making computing their spectral information a considerable challenge. This paper describes data-driven algorithms with rigorous convergence guarantees for computing spectral information of Koopman operators from trajectory data. We introduce residual dynamic mode decomposition (ResDMD), which provides the first scheme for computing the spectra and pseudospectra of general Koopman operators from snapshot data without spectral pollution. Using the resolvent operator and ResDMD, we also compute smoothed approximations of spectral measures associated with measure-preserving dynamical systems. We prove explicit convergence theorems for our algorithms, which can achieve high-order convergence even for chaotic systems, when computing the density of the continuous spectrum and the discrete spectrum. We demonstrate our algorithms on the tent map, Gauss iterated map, nonlinear pendulum, double pendulum, Lorenz system, and an $11$-dimensional extended Lorenz system. Finally, we provide kernelized variants of our algorithms for dynamical systems with a high-dimensional state-space. This allows us to compute the spectral measure associated with the dynamics of a protein molecule that has a 20,046-dimensional state-space, and compute nonlinear Koopman modes with error bounds for turbulent flow past aerofoils with Reynolds number $>10^5$ that has a 295,122-dimensional state-space

Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems

Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands out as the poster child of projection-based methods. Although the Koopman operator itself is linear, the fact that it acts in an infinite-dimensional space of observables poses various challenges. These include spurious modes, essential spectra, and the verification of Koopman mode decompositions. While recent work has addressed these challenges for deterministic systems, there remains a notable gap in verified DMD methods tailored for stochastic systems, where the Koopman operator measures the expectation of observables. We show that it is necessary to go beyond expectations to address these issues. By incorporating variance into the Koopman framework, we address these challenges. Through an additional DMD-type matrix, we approximate the sum of a squared residual and a variance term, each of which can be approximated individually using batched snapshot data. This allows verified computation of the spectral properties of stochastic Koopman operators, controlling the projection error. We also introduce the concept of variance-pseudospectra to gauge statistical coherency. Finally, we present a suite of convergence results for the spectral quantities of stochastic Koopman operators. Our study concludes with practical applications using both simulated and experimental data. In neural recordings from awake mice, we demonstrate how variance-pseudospectra can reveal physiologically significant information unavailable to standard expectation-based dynamical models

Confinement and Strings in MQCD

We study aspects of confinement in the M theory fivebrane version of QCD (MQCD). We show heavy quarks are confined in hadrons (which take the form of membrane-fivebrane bound states) for N=1 and softly broken N=2 SU(Nc) MQCD. We explore and clarify the transition from the exotic physics of the latter to the standard physics of the former. In particular, the many strings and quark-antiquark mesons found in N=2 field theory by Douglas and Shenker are reproduced. It is seen that in the N=1 limit all but one such meson disappears while all of the strings survive. The strings of softly broken N=2, N=1, and even non-supersymmetric SU(Nc) MQCD have a common ratio for their tensions as a function of the amount of flux they carry. We also comment on the almost BPS properties of the Douglas-Shenker strings and discuss the brane picture for monopole confinement on N=2 QCD Higgs branches.Comment: 39 pages, 17 figures, uses harvma

Multiple approaches to microbial source tracking in tropical northern Australia

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in MicrobiologyOpen 3 (2014): 860–874, doi:10.1002/mbo3.209.Microbial source tracking is an area of research in which multiple approaches are used to identify the sources of elevated bacterial concentrations in recreational lakes and beaches. At our study location in Darwin, northern Australia, water quality in the harbor is generally good, however dry-season beach closures due to elevated Escherichia coli and enterococci counts are a cause for concern. The sources of these high bacteria counts are currently unknown. To address this, we sampled sewage outfalls, other potential inputs, such as urban rivers and drains, and surrounding beaches, and used genetic fingerprints from E. coli and enterococci communities, fecal markers and 454 pyrosequencing to track contamination sources. A sewage effluent outfall (Larrakeyah discharge) was a source of bacteria, including fecal bacteria that impacted nearby beaches. Two other treated effluent discharges did not appear to influence sites other than those directly adjacent. Several beaches contained fecal indicator bacteria that likely originated from urban rivers and creeks within the catchment. Generally, connectivity between the sites was observed within distinct geographical locations and it appeared that most of the bacterial contamination on Darwin beaches was confined to local sources

The narratives of Hardship: : The new and the old poor in the aftermath of the 2008 crisis in Europe

This document is the Accepted Manuscript version of the following article: Hulya Dagdeviren, Matthew Donoghue, and Lars Meier, ‘The narratives of hardship: the new and the old poor in the aftermath of the 2008 crisis in Europe’, The Sociological Review, vol. 65 (2): 369-385, May 2017. The final, definitive version of record is available online at doi: https://doi.org/10.1111/1467-954X.12403. Published by SAGE.This paper examines poverty and hardship in Europe after the 2008 crisis, using household interviews in nine European countries. A number of findings deserve highlighting. First, making a distinction between ‘the old poor’ (those who lived in poverty before as well as after the crisis) and ‘the new poor’ (thosewho fell into hardship after the crisis), we show that hardship is experienced quite differently by these groups. Second, the household narratives showed that while material deprivations constitute an important aspect of hardship, the themes of insecurity and dependency also emerged as fundamental dimensions. In contrast to popular political discourse in countries such as the UK, dependency on welfare or family was experienced as a source of distress and manifested as a form of hardship by participants in all countries covered in this study.Peer reviewedFinal Accepted Versio

Functionalized micro-capillary film for the rapid at-line analysis of IgG aggregates in a cell culture bioreactor.

A micro-capillary film has been developed that offers the potential for an at-line analytical tool for rapid aggregate analysis during biopharmaceutical antibody production. A non-porous walled micro-capillary film (NMCF) with cation exchange functionality was demonstrated to act as a chromatography medium that could be operated with high linear fluid velocities and was highly resistant to blockage by entrained particulates, including cells. The NMCF containing 19 parallel microcapillaries was prepared using a melt extrusion process from poly(ethylene-vinyl alcohol) copolymer (EVOH). The NMCF-EVOH was modified to have cation-exchange functionality (NMCF-EVOH-SP) and shown to differentially bind monomer and aggregated species of IgG antibody directly from a bioreactor. The use of NMCF-EVOH-SP to quantify aggregate concentrations in monoclonal antibody preparations in less than 20 minutes was demonstrated.The authors would like to thank the EPSRC for the provision of a CASE Award. This study was sponsored by MedImmune, the global biologics R&D arm of AstraZeneca.This is the final version of the article. It first appeared from Taylor & Francis via http://dx.doi.org/10.1080/19420862.2015.106536

Ami - The Chemist's Amanuensis

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.Abstract The Ami project was a six month Rapid Innovation project sponsored by JISC to explore the Virtual Research Environment space. The project brainstormed with chemists and decided to investigate ways to facilitate monitoring and collection of experimental data. A frequently encountered use-case was identified of how the chemist reaches the end of an experiment, but finds an unexpected result. The ability to replay events can significantly help make sense of how things progressed. The project therefore concentrated on collecting a variety of dimensions of ancillary data - data that would not normally be collected due to practicality constraints. There were three main areas of investigation: 1) Development of a monitoring tool using infrared and ultrasonic sensors; 2) Time-lapse motion video capture (for example, videoing 5 seconds in every 60); and 3) Activity-driven video monitoring of the fume cupboard environs. The Ami client application was developed to control these separate logging functions. The application builds up a timeline of the events in the experiment and around the fume cupboard. The videos and data logs can then be reviewed after the experiment in order to help the chemist determine the exact timings and conditions used. The project experimented with ways in which a Microsoft Kinect could be used in a laboratory setting. Investigations suggest that it would not be an ideal device for controlling a mouse, but it shows promise for usages such as manipulating virtual molecules.Peer Reviewe

Mapping Species Composition of Forests and Tree Plantations in Northeastern Costa Rica with an Integration of Hyperspectral and Multitemporal Landsat Imagery

An efficient means to map tree plantations is needed to detect tropical land use change and evaluate reforestation projects. To analyze recent tree plantation expansion in northeastern Costa Rica, we examined the potential of combining moderate-resolution hyperspectral imagery (2005 HyMap mosaic) with multitemporal, multispectral data (Landsat) to accurately classify (1) general forest types and (2) tree plantations by species composition. Following a linear discriminant analysis to reduce data dimensionality, we compared four Random Forest classification models: hyperspectral data (HD) alone; HD plus interannual spectral metrics; HD plus a multitemporal forest regrowth classification; and all three models combined. The fourth, combined model achieved overall accuracy of 88.5%. Adding multitemporal data significantly improved classification accuracy (p less than 0.0001) of all forest types, although the effect on tree plantation accuracy was modest. The hyperspectral data alone classified six species of tree plantations with 75% to 93% producer's accuracy; adding multitemporal spectral data increased accuracy only for two species with dense canopies. Non-native tree species had higher classification accuracy overall and made up the majority of tree plantations in this landscape. Our results indicate that combining occasionally acquired hyperspectral data with widely available multitemporal satellite imagery enhances mapping and monitoring of reforestation in tropical landscapes

Smart Cities: Towards a New Citizenship Regime? A Discourse Analysis of the British Smart City Standard

Growing practice interest in smart cities has led to calls for a less technology-oriented and more citizen-centric approach. In response, this articles investigates the citizenship mode promulgated by the smart city standard of the British Standards Institution. The analysis uses the concept of citizenship regime and a mixture of quantitative and qualitative methods to discern key discursive frames defining the smart city and the particular citizenship dimensions brought into play. The results confirm an explicit citizenship rationale guiding the smart city (standard), although this displays some substantive shortcomings and contradictions. The article concludes with recommendations for both further theory and practice development

KDOQI US Commentary on the 2017 ACC/AHA Hypertension Guideline

Hypertension is a modifiable risk factor for cardiovascular morbidity and mortality and reduction of elevated blood pressure (BP) remains an important intervention for slowing kidney disease progression. Over the past decade, the most appropriate BP target for initiation and titration of BP-lowering medications has been an area of intense research and debate within the clinical community. In 2017, the American College of Cardiology and the American Heart Association (ACC/AHA) in conjunction with several other professional societies released new hypertension guidelines based on data from a systematic review of clinical trials and observational data. While many of the recommendations in the ACC/AHA hypertension guideline are relevant to nephrology practice, BP targets and management strategies for patients receiving dialysis are not discussed. This Kidney Disease Outcomes Quality Initiative (KDOQI) commentary focuses largely on recommendations from the ACC/AHA hypertension guidelines that are pertinent to individuals at risk of chronic kidney disease or with non–dialysis-dependent chronic kidney disease. This KDOQI commentary also includes a brief discussion of the consensus statement regarding hypertension diagnosis and management for adults receiving maintenance dialysis published by the European Renal and Cardiovascular Medicine Working Group of the European Renal Association–European Dialysis and Transplant Association (ERA-EDTA) and the Hypertension and the Kidney working group of the European Society of Hypertension. Overall, we support the vast majority of the ACC/AHA recommendations and highlight select areas in which best diagnosis and treatment options remain controversial